Function a

L

Loki123

Full Member
Joined
Sep 22, 2021
Messages
790
I did this and did it apparently correctly. However, I don't get it. Why is a calculated through x?? IMG_20220505_192633.jpg
 
As before, start with definitions. What makes a function continuous at a given point?
 
Loki123 said:
so no holes, asimptotes, jumps... i still don't get how a relates to it
Click to expand...
So what does f(4) have to be for the f(x) to be continuous?

Simple example: Take
[imath]f(x) = \begin{cases} x + 3 & x \neq 4 \\ a & x = 4 \end{cases}[/imath]

What would a have to be to "plug the hole" in x + 3 when x = 4?

-Dan
 
topsquark said:
So what does f(4) have to be for the f(x) to be continuous?

Simple example: Take
[imath]f(x) = \begin{cases} x + 3 & x \neq 4 \\ a & x = 4 \end{cases}[/imath]

What would a have to be to "plug the hole" in x + 3 when x = 4?

-Dan
Click to expand...
a=4?
 
Once again, you have not told us the exact problem. You said [imath]f(x) = a \text { if } x \ne 4.[/imath]
But we know what you intended. PLease be careful in the statements of problems; we cannot always see how to correct them..

"No holes, no vertical asymptotes, and no jumps" is a good informal definition, but the way to make the "no jumps" part of that definition mathematically exact is with limits as was said in post 6.

With respect to post 7:

[math]\lim_{x \rightarrow 4}(x + 3) = \text {WHAT?}[/math]
 
JeffM said:
Once again, you have not told us the exact problem. You said [imath]f(x) = a \text { if } x \ne 4.[/imath]
But we know what you intended. PLease be careful in the statement of the problem.

"No holes, no vertical asymptotes, and no jumps" is a good informal definition, but the way to make the "no jumps" mathematically exact is with limits as was said in post 6.

With respect to post 7:

[math]\lim_{x \rightarrow 4}(x + 3) = WHAT?[/math]
Click to expand...
 
JeffM said:
Once again, you have not told us the exact problem. You said [imath]f(x) = a \text { if } x \ne 4.[/imath]
But we know what you intended. PLease be careful in the statements of problems; we cannot always see how to correct them..

"No holes, no vertical asymptotes, and no jumps" is a good informal definition, but the way to make the "no jumps" part of that definition mathematically exact is with limits as was said in post 6.

With respect to post 7:

[math]\lim_{x \rightarrow 4}(x + 3) = \text {WHAT?}[/math]
Click to expand...
infinity? but that would be a vertical asymptote ?
 
Loki123 said:
infinity? but that would be a vertical asymptote ?
Click to expand...
Loki123, you have asked questions about Calculus. The first thing they teach you in Calculus is limits. Let me say [imath]\lim_{x \to 4} (x + 3)[/imath] in words: the limit of the function x + 3 as x gets close to 4. So what is [imath]\lim_{x \to 4} (x + 3)[/imath] again?

-Dan
 
topsquark said:
Loki123, you have asked questions about Calculus. The first thing they teach you in Calculus is limits. Let me say [imath]\lim_{x \to 4} (x + 3)[/imath] in words: the limit of the function x + 3 as x gets close to 4. So what is [imath]\lim_{x \to 4} (x + 3)[/imath] again?

-Dan
Click to expand...
7
 
You must log in or register to reply here.
Top